 HELLO FRIENDS I am S.R. Dhulange working as an associate professor in the department of mechanical engineering at Vulture Institute of Technology, Sholapur. Today we are going to discuss on work piece control theory. Now this work piece control theory is related with tool engineering as well as process engineering. Now we are taking this particular topic in process engineering. Learning Outcome Students will be acquainted with work piece control theory and understand 3-1 principle of location for process planning. Now under work piece control theory the first we are going to see what is 3-1 principle and what is redundant. Now under work piece control theory the 3-1 location system or the concept of location we are going to discuss based on the flat configuration work pieces. Now what is the location? Location is nothing but to maintain a dimensional and position relationship between the work piece and the cutting tool. And what is the meaning of the locator? Locator is an element which is used for the location. Now in order to constrain the degrees of freedom for a particular work piece when we are doing operation we require the location along with clamping. Now this is a cube wherein we are assuming that this is in space. Now when we are assuming this work piece is in space. So this is the x-axis of the work piece, this is the y-axis of the work piece and this is the z-axis of the work piece. Now how many moments will be there for this particular cube? Now along x-axis there will be two moments. Here I can say this is one side, this is another side. Along y-y there are two moments, one is upward, another is downward. Along z there are two moments, this one and that one. So along the each axis there will be six moments and these moments are called as moment of translation. So similarly along each axis there will be some moment of rotation. Now this moment of rotation is divided in two. Two that is one is clockwise, another is anticlockwise. So along x-axis there is one clockwise, one anticlockwise. Along y-axis there is one clockwise, another is anticlockwise. Along z-axis one clockwise and along z-axis one is anticlockwise. So there will be six moments of rotation. So you know there are six moments of translation and six moments of rotation. This is called as a twelve degree of freedom. Now in order to constrain these twelve degrees of freedom we have to make use of the locator and the clamp. Now here three to one principle suggest that you can take three mutually perpendicular planes in order to constrain some degrees of freedom. So that is shown here in this view. Now here one locator is taken at the bottom plane. This is the front view and this is the top view. So this is a rectangle indicates a symbol for the locator. Now this is a side view for that. Now because of this one locator it stops a linear moment downward along y-axis because the locator is kept at the bottom of the workpiece. Now the second locator is taken again at the bottom surface. So second locator stops the rotation about axis z-z. Now this is shown here one and two locators. So these are the two locators which are taken at the bottom. One more locator is taken at the bottom in order to see how many moments are restricted. So this is one, two and three. So when we take these three locators at the bottom so what will happen? The workpiece will not rotate along the x-axis. Similarly it will not rotate along the z-axis and it will not go in downward direction along the y-axis. Means by making use of these three points or these three locations we can constrain five degrees of freedom. One is x-axis rotation along x-axis clock anticlockwise rotation along z-axis clock anticlockwise and the moment of translation that is the locator will not allow the workpiece to come at the bottom. So it will constrain five degrees of freedom. Now next is this is three. Now why we have taken three pins? If suppose we take two what will happen? There is a possibility that the workpiece may rotate along either clock or anticlockwise because of the position of that locator. So that's why we are not going to take two locators at the bottom. Now because of the three we are going to get a plane because the plane passes through the three points. If suppose we take a fourth locator. Now the fourth locator at the bottom plane. What will happen? It will be unnecessary. There is no need for that particular location. So this is called redundant. Now so this is the first plane which is taken in order to constrain five degrees of freedom. Now the next plane is taken that is a perpendicular to the bottom plane. So this is the bottom plane and these are the two location points which are perpendicular to the bottom plane. Now because of these two what will happen? So this workpiece will not move in left direction. So this is a direction from my side it is a left. So it will not move along left direction. And this is axis y axis. So here this vertical axis is a y axis. Because of the plane this is a plane which we have taken in order to have a location by means of two points. So there will not be any rotation along this y axis. So there is no rotation along y axis. Either it is a clock or anti clock. And there is no movement towards the left side. So because of these two pins what will happen? We can constrain three degrees of freedom. That is the rotation along y y that is clock and anti. And one is the left side. Now these principles suggest that go for three mutually perpendicular planes. Now this is a plane which we have taken that is a bottom plane. And the second plane which we have taken that is a perpendicular to the bottom plane. So this bottom plane is having three point location. And the perpendicular plane to the bottom plane is having the two point location or the two locators. Now because of this bottom three pins and because of this side two pins we could able to constrain eight degrees of freedom. Now three mutually perpendicular planes are taken. In that case the third plane will be this one that is here it indicates six. So one two and three which are at the bottom. So this dot indicates on the triangle is that is the pins are kept at the bottom side. And fourth fifth that is the plane which is perpendicular to the bottom plane. And the third mutually perpendicular plane here this is a sixth locator. Because of this what will happen it will not move away from me in this way. So it will constrain one degree of freedom means what by making use of three pins at the bottom two pins at the another plane which is perpendicular to the bottom plane and the sixth pin which is mutually perpendicular to both the planes we could able to constrain five plus three plus one that is nine degree of freedom. Now here one more seventh pin is shown this is called as redundant as I already told. Now here the sixth is taken if suppose we take sixth and seventh on this plane it is not necessary because this sixth is constrain only one degree of freedom. So this is what a three to one principle which is required in the process engineering in order to have a planning for the process. Now these are the references. Thank you.